Let $A\in M_{n}(\mathbb{R})$ and $B\in\mathbb{R}^{n}$ s.t. $(A,B)$ is Controllable. Then $\exists T\in M_{n}(\mathbb{R})$ with $\det(T)\not=0$ s.t. $$TAT^{-1}=\begin{bmatrix}0 & 1 & 0 & \dots & 0 \\ 0 & 0 & 1 & \dots & 0 \\ \vdots & \vdots & \vdots & & \vdots \\ -a_{0} & -a_{1} & -a_{2} & \dots & -a_{n-1}\end{bmatrix}\quad TB=\begin{bmatrix}0 \\ 0 \\ \vdots \\ 1\end{bmatrix}$$where $a_{i}\in\mathbb{R}$ (i.e. there exists a Weighting Pattern that yields a controllability canonical form).